3.2-08 Projections and collapse

Projections and collapse — linear algebra practice

Construct coordinate and line projections, compute their outputs and identify erased directions. Compare orthogonal projection with an oblique projection, explain repeated projection, and examine a plane specified by its normal. The exercises connect the retained component with the information that cannot be recovered.

What you will practise

• Compute line and plane projections
• Identify image and erased directions
• Distinguish orthogonal and oblique projection

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review dot products, coordinate subspaces and basis images. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to reason about information loss and injectivity.